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Diagrammatica : The Path to Feynman Diagrams - Martinus Veltman

Diagrammatica

The Path to Feynman Diagrams

Paperback

Published: 15th August 1994
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This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. The book begins with a brief review of some aspects of Einstein's theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques learned in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions on renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. An appendix containing a comprehensive summary of the rules and conventions used is followed by an appendix specifying the full Lagrangian of the Standard Model and the corresponding Feynman rules. To make the book useful for a wide audience a final appendix provides a discussion on the metric used, and an easy to use dictionary connecting equations written with different metric. Written as a textbook, many diagrams and examples are included.

"...a masterful introduction to quantum field theory and its application to elementary particle physics through Feynman diagrams. The approach is constructive rather than deductive, and the book offers many fine insights into the physics content of results that may be thought of as purely mathematical." Ernest Ma and Jose Wudka, Physics Today "...would be a useful and solid starting point for a novice field theorist..." R. Delbourgo, Mathematical Reviews

Introductionp. xi
Lorentz and Poincare Invariancep. 1
Lorentz Invariancep. 1
Structure of the Lorentz Groupp. 7
Poincare Invariancep. 10
Maxwell Equationsp. 10
Notations and Conventionsp. 12
Relativistic Quantum Mechanics of Free Particlesp. 15
Hilbert Spacep. 15
Matrices in Hilbert Spacep. 22
Fieldsp. 25
Structure of Hilbert Spacep. 29
Interacting Fieldsp. 32
Physical Systemp. 32
Hilbert Spacep. 33
Magnitude of Hilbert Spacep. 34
U-matrix, S-matrixp. 35
Interpolating Fieldsp. 39
Feynman Rulesp. 46
Feynman Propagatorp. 54
Scattering Cross Sectionp. 55
Lifetimep. 60
Numerical Evaluationp. 62
Schrodinger Equation, Bound Statesp. 62
Particles with Spinp. 68
Representations of the Lorentz Groupp. 68
The Dirac Equationp. 76
Fermion Fieldsp. 79
The E.M. Fieldp. 85
Quantum Electrodynamicsp. 87
Charged Vector Boson Fieldsp. 91
Electron-Proton Scattering. The Rutherford Formulap. 92
Explorationsp. 98
Scattering Cross Section for e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript -]p. 98
Pion Decay. Two Body Phase Space. Cabibbo Anglep. 101
Vector Boson Decayp. 105
Muon Decay. Fiertz Transformationp. 108
Hyperon Leptonic Decayp. 117
Pion Decay and PCACp. 124
Neutral Pion Decay and PCACp. 131
Renormalizationp. 137
Introductionp. 137
Loop Integralsp. 137
Self Energyp. 145
Power Countingp. 148
Quantum Electrodynamicsp. 151
Renormalizable Theoriesp. 153
Radiative Corrections: Lamb Shiftp. 154
Radiative Corrections: Top Correction to [rho]-Parameterp. 157
Neutral Pion Decay and the Anomalyp. 162
Massive and Massless Vector Fieldsp. 169
Subsidiary Condition Massive Vector Fieldsp. 169
Subsidiary Condition Massless Vector Fieldsp. 171
Photon Helicitiesp. 173
Propagator and Polarization Vectors of Massive Vector Particlesp. 174
Photon Propagatorp. 177
Left Handed Photonsp. 180
Unitarityp. 183
U-matrixp. 183
Largest Time Equationp. 185
Cutting Equationsp. 187
Unitarity and Cutting Equationp. 191
Unitarity: General Casep. 197
Kallen-Lehmann Representation, Dispersion Relationp. 200
Momenta in Propagatorsp. 204
Quantum Electrodynamics: Finallyp. 207
Unitarityp. 207
Ward Identitiesp. 208
Complex Spaces, Matrices, CBH Equationp. 213
Basicsp. 213
Differentiation of Matricesp. 217
Functions of Matricesp. 218
The CBH Equationp. 220
Tracesp. 224
Generalp. 224
Multi-Dimensional [gamma]-Matricesp. 230
Frequently Used Equationsp. 231
Dimensional Regularizationp. 233
Summary: Combinatorial Factorsp. 243
Summaryp. 243
External Lines, Spin Sums, Propagatorsp. 245
Combinatorial Factorsp. 247
Standard Modelp. 249
Lagrangianp. 249
Feynman Rulesp. 258
Metric and Conventionsp. 273
General Considerationsp. 273
Translation Examplesp. 279
Translation Dictionaryp. 281
Indexp. 282
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521456920
ISBN-10: 0521456924
Series: Cambridge Lecture Notes in Physics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 300
Published: 15th August 1994
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.22 x 15.14  x 2.01
Weight (kg): 0.45